Names of 3 dimensional space groups - nwchemgit/nwchem GitHub Wiki

Names of 3-dimensional space groups

Web resources:

  • NRL Crystal Lattice Structures 2

For many of the space groups there are multiple choices of symmetry transformations. They are denoted as settings for each of the groups. By default, the code will use the first setting. By defining setting <integer setting> on the symmetry input line (see Symmetry Group Input paragraph), you can tell the code to choose a different setting/symmetry transformation.

Triclinic space groups (group numbers: 1-2)

P1 P-1

Monoclinic space groups (group numbers: 3-15)

P2 P2_1 C2
Pm Pc Cm Cc P2/m
P2_1/m C2/m P2/c P2_1/c C2/c

Orthorhombic space groups (group numbers: 16-74)

P222 P222_1 P2_12_12 P2_12_12_1 C222_1
C222 F222 I222 I2_12_12_1 Pmm2
Pmc2_1 Pcc2 Pma2 Pca2_1 Pnc2
Pmn2_1 Pba2 Pna2_1 Pnn2 Cmm2
Cmc2_1 Ccc2 Amm2 Abm2 Ama2
Aba2 Fmm2 Fdd2 Imm2 Iba2
Ima2 Pmmm Pnnn Pccm Pban
Pmma Pnna Pmna Pcca Pbam
Pccn Pbcm Pnnm Pmmn Pbcn
Pbca Pnma Cmcm Cmca Cmmm
Cccm Cmma Ccca Fmmm Fddd
Immm Ibam Ibca Imma

Tetragonal space groups (group numbers: 75-142)

P4
P4_1 P4_2 P4_3 I4 I4_1
P-4 I-4 P4/m P4_2/m P4/n
P4_2/n I4/m I4_1/a P422 P42_12
P4_122 P4_12_12 P4_222 P4_22_12 P4_322
P4_32_12 I422 I4_122 P4mm P4bm
P4_2cm P4_2nm P4cc P4nc P4_2mc
P4_2bc I4mm I4cm I4_1md I4_1cd
P-42m P-42c P-42_1m P-42_1c P-4m2
P-4c2 P-4b2 P-4n2 I-4m2 I-4c2
I-42m I-42d P4/mmm P4/mcc P4/nbm
P4/nnc P4/mbm P4/mnc P4/nmm P4/ncc
P4_2/mmc P4_2/mcm P4_2/nbc P4_2/nnm P4_2/mbc
P4_2/mnm P4_2/nmc P4_2/ncm I4/mmm I4/mcm
I4_1/amd I4_1/acd

Trigonal space groups (group numbers: 143-167)

P3 P3_1 P3_2
R3 P-3 R-3 P312 P321
P3_112 P3_121 P3_212 P3_221 R32
P3m1 P31m P3c1 P31c R3m
R3c P-31m P-31c P-3m1 P-3c1
R-3m R-3c

Hexagonal space groups (group numbers: 168-194)

P6 P6_1 P6_5
P6_2 P6_4 P6_3 P-6 P6/m
P6_3/m P622 P6_122 P6_522 P6_222
P6_422 P6_322 P6mm P6cc P6_3cm
P6_3mc P-6m2 P-6c2 P-62m P-62c
P6/mmm P6/mcc P6_3/mcm P6_3/mmc

Cubic space groups (group numbers: 195-230)

P23
F23 I23 P2_13 I2_13 Pm-3
Pn-3 Fm-3 Fd-3 Im-3 Pa-3
Ia-3 P432 P4_232 F432 F4_132
I432 P4_332 P4_132 I4_132 P-43m
F-43m I-43m P-43n F-43c I-43d
Pm-3m Pn-3n Pm-3n Pn-3m Fm-3m
Fm-3c Fd-3m Fd-3c Im-3m Ia-3d